Abstract:

According to the disclosed is a method for controlling taper tension in
the winding section of a web handling system, a more stable, high-quality
wound roll can be produced by stabilizing radial stress distribution and
minimizing telescoping, which is the lateral displacement of material in
the winding section, using either hybrid taper tension control through a
hybrid factor (α) or heaviside taper tension control through a
heaviside factor (φ), in the winding process, which is the final
section of the roll-to-roll or web handling system.

Claims:

1. A method for controlling taper tension in the winding section of a web
handling system, the method comprising the steps of:(a) inputting into
PLC a material to be used in initial operation, along with operating
tension and velocity;(b) transmitting the diameter value (data) of a
roll, currently being wound, from a motor driver into the PLC;(c)
establishing in the PLC a taper value (reduction in operating tension) to
be achieved;(d) determining in the PLC the type of taper tension profile
in consideration of the radial stress distribution and telescoping within
the roll on the basis of data, including initial operating tension, roll
diameter and taper value, which are collected from steps (a) to (c);
and(e) producing in the PLC an electrical signal for taper tension
according to the taper type determined in step (d) to control the
pressure of the air cylinder of a dancer system through an E/P converter
and to control taper tension through a tension meter or a loadcell, in
which the taper tension control method satisfies the following equation:
σ w ( r ) = σ 0 [ 1 - ( taper 100 ) (
r - 1 ) { r + α ( R - r - 1 ) } ] ##EQU00015##
wherein the hybrid factor serves to select one of a linear taper tension
profile and a hyperbolic taper tension profile based on an value between
1 and 0 and produces a taper tension profile, which is an intermediate
type between the linear taper tension profile and the hyperbolic taper
tension profile.

2. A method for controlling taper tension in the winding section of a web
handling system, the method comprising the steps of:(a) inputting into
PLC a material to be used in initial operation, along with operating
tension and velocity;(b) transmitting the diameter value (data) of a
roll, currently being wound, from a motor driver into the PLC;(c)
establishing in the PLC a taper value (reduction in operating tension) to
be achieved;(d) determining in the PLC the type of taper tension profile
in consideration of the radial stress distribution and telescoping within
the roll on the basis of data, including initial operating tension, roll
diameter and taper value, which are collected from steps (a) to (c);
and(e) producing in the PLC an electrical signal for taper tension
according to the taper type determined in step (d) to control the
pressure of the air cylinder of a dancer system through an E/P converter
and to control taper tension through a tension meter or a loadcell, in
which the taper tension control method satisfies the following equation:
σ w ( r ) = σ 0 [ 1 - ( taper 100 ) (
r - 1 ) { r + ( R - r - 1 ) [ 1 - Φ ( r - τ )
] } ] ##EQU00016## Φ ( r - τ ) = { 0
r < τ 1 r ≧ τ ##EQU00016.2## wherein the
taper tension profile is changed depending on the value of Φ.

3. The method of claim 2, wherein the type of linear taper tension profile
is changed to the type of hyperbolic taper tension profile depending on
the value of Φ.

4. A method for controlling taper tension in the winding section of a web
handling system, the method comprising the steps of:(a) inputting into
PLC a material to be used in initial operation, along with operating
tension and velocity;(b) transmitting the diameter value (data) of a
roll, currently being wound, from a motor driver into the PLC;(c)
establishing in the PLC a taper value (reduction in operating tension) to
be achieved;(d) determining in the PLC the type of taper tension profile
in consideration of the radial stress distribution and telescoping within
the roll on the basis of initial operating tension, roll diameter and
taper value, which are collected from steps (a) to (c); and(e) producing
in the PLC an electrical signal for taper tension according to the taper
type determined in step (d) to control the pressure of the air cylinder
of a dancer system through an E/P converter and to control taper tension
through a tension meter or a loadcell, in which the taper tension control
method satisfies the following equation: σ w ( r ) =
σ 0 [ 1 - ( taper 100 ) ( r - 1 ) { r + α
( R - r - 1 ) } ] ##EQU00017## or ##EQU00017.2##
σ w ( r ) = σ 0 [ 1 - ( taper 100 ) (
r - 1 ) { r + ( R - r - 1 ) [ 1 - Φ ( r - τ )
] } ] ##EQU00017.3## Φ ( r - τ ) = { 0
r < τ 1 r ≧ τ ##EQU00017.4##

5. The method of claim 4, wherein the hybrid factor serves to select one
of a linear taper tension profile and a hyperbolic taper tension profile
at an value between 1 and 0 and produces a taper tension profile, which
is an intermediate type between the linear taper tension profile and the
hyperbolic taper tension profile.

6. The method of claim 4, wherein the taper tension profile is changed
depending on the value of Φ.

Description:

TECHNICAL FIELD

[0001]The present invention relates to a method for controlling taper
tension in the winding section of a web handling system, and more
particularly to a method for controlling taper tension in the winding
section of a web handling system, which can produce a more uniform,
high-quality wound roll to be produced by stabilizing radial stress
distribution and minimizing telescoping, which is the lateral
displacement of material in the winding section.

BACKGROUND ART

[0002]In general, a web handling or roll-to-roll system refers to a system
in which a web of a material having a width and length significantly
larger than thickness, such as a plastic film or a thick iron sheet
material, passes through rolls, while it is continuously subjected to
various processes.

[0003]Among the production sections of the web handling system, the
winding section is an important process. A process for producing
center-wound rolls has advantages in that it is efficient, provides a
large storage space and is very convenient in high-speed operations.
However, the non-uniform stresses within the rolls can cause damages such
as buckling, spoking, cinching, etc. For this reason, a winding process,
which avoids the occurrence of excessive or unnecessary internal stress
and induces stable stress distribution, is required.

[0004]With respect to prior papers, Altmann presented a general solution
for a linear elastic roll material while using a nonlinear constitutive
relation to find the radial and hoop stresses for successive wraps [4].
In addition, Altmann proposed a second-order differential equation for
the linear elastic material in a center-wound roll.

[0005]Yagoda established the core compliance as an inner boundary
condition on center-wound rolls [5], and Hakiel incorporated nonlinear
material properties into the basic mechanics and numerical solutions of
wound roll stresses [3].

[0007]They noted that the model typically predicted stresses that were
twice as large as their measured values. However, they were able to bring
predicted and measured values into better agreement by modifying the
outer hoop-stress boundary condition to relax relative to the out-layer
tensile stresses by their model of "wound on tension" loss.

[0008]Burns et al. derived a strain-based formula for stresses in profiled
centre wound rolls by using a residual stress model [1]. They noted that
radial stress within wound rolls is closely related to the variation of
effective residual stress.

[0009]The present inventors have found that a momentous factor for making
a high quality wound roll is the taper tension profile of the winding
process. Also, in the present invention, an auto taper tension profile
making method for avoiding the damage (telescoping, buckling, cinching,
etc.) is presented. The experimental results revealed that the proposed
method is very useful.

[0010]FIG. 1 is a schematic diagram of the tension T acting on the web and
roll. In FIG. 1, "a" is a core radius, "R" is the current radius of the
roll, "M" is torque, and ".sup.δω" is a taper tension
profile.

[0011]In general, a linear taper tension profile and a hyperbolic taper
tension profile are applied to winding processes [2][3]. Herein, the
linear taper tension profile is a profile in which tension linearly
decreases with an increase in the radius of the roll, and the hyperbolic
taper tension profile is a profile in which tension hyperbolically
decreases with an increase in the radius of the roll.

[0012]The linear and hyperbolic taper tension profiles are represented by
the following Math Figures 1 and 2, wherein ".sup.σ0" is initial
web stress, taper is the decrement for taper tension, and r is
dimensionless roll radius ratio, i.e., the value obtained by dividing the
roll radius by the core radius:

[0013]FIG. 2 shows the taper tension plotted as a taper tension ratio,
i.e., (σw(r)/σ0), for the two profiles. The
hyperbolic taper tension variation is larger at the core and smaller
toward the outer layer, but the linear taper tension variation is
constant.

[0014]The boundary condition is that the outside of the roll is stress
free.

[0015]Thus, stress for the radial direction within the wound roll is given
in Math Figure 3 [1].

[0018]FIG. 3 shows the radial stresses plotted as a
-σ.sub.α/σ0 for the two taper tension profiles. On
the whole, the radial stress distribution for the hyperbolic profile has
equipollence more than for the linear taper stress.

[0019]FIG. 4 shows the variation of the ERS value for the two tension
profiles. In FIGS. 3 and 4, the close correlation between ERS and the
radial stress can be found. As the derivative of the ERS value is low,
the distribution of the radial stress is small and equal.

[0020]On the basis of the above results, it is found that the hyperbolic
taper tension profile prevents intensive increment of the radial stress
and promotes uniform radial stress distribution.

[0021]Camber can be expressed as the radius of the curvature in the
un-tensioned condition and lying on a flat surface. Assuming linear
stress distribution in the cambered web as shown in FIG. 5, the induced
moment can be found in Math Figure 8:

[0026]In Math Figure 11, yL is equal to telescoping error in a
winding process, because the downstream roller is a wound roll.
Therefore, through the correlation between lateral deflection and tension
distribution, the mathematical model for telescoping can be defined as
shown in Math Figure 12:

[0027]wherein K is stiffness coefficient, F is force given by web tension,
and is wrap angle. FIG. 7 shows computer simulation results for the
correlation between taper tension and lateral displacement for nonuniform
tension distribution in the width direction of a material. FIG. 7 shows
that two taper tension profiles, which show different changes in tension,
are related to the occurrence of telescoping with an increase in radius.

[0028]FIG. 8 is a photograph showing a telescoping phenomenon in a prior
wound roll, and FIG. 9 is a photograph showing a starring phenomenon in a
prior wound roll.

[0029]As shown in FIGS. 8 and 9, the term "telescoping" refers to the
widthwise displacement of material in a finally produced roll, and the
term "starring" refers to star-shaped damage caused at the side of a roll
due to non-uniform stress distribution. Telescoping and starring greatly
influence the quality of a roll.

[0030]In a taper tension control method, which is a tension control method
according to the prior art, telescoping in the beginning of rewinding can
be minimized, but great radial stress occurs. In comparison with this, in
a hyperbolic tension control method, telescoping in the beginning of
rewinding is serious, but radial stress distribution is low.

DISCLOSURE

Technical Problem

[0031]The present invention has been made in order to solve the
above-described problems occurring in the prior art, and a first object
of the present invention is to provide a method for controlling taper
tension in the winding section of a web handling system, which can
produce a more uniform, high-quality wound roll by stabilizing radial
stress distribution and minimizing telescoping, which is the lateral
displacement of material in the winding section.

[0032]A second object of the present invention is to provide a method for
controlling taper tension in the winding section of a web handling
system, which can achieve the stabilization of radial stress distribution
and the minimization of telescoping using either hybrid taper tension
control through a hybrid factor (α (alpha)) or heaviside taper
tension control through a heaviside factor (Φ), in the winding
process, which is the final section of the roll-to-roll or web handling
system.

[0033]A third object of the present invention is to a method for
controlling taper tension in the winding section of a web handling
system, which can achieve the stabilization of radial stress distribution
and the minimization of telescoping using either hybrid taper tension
control through a hybrid factor (α (alpha)) or heaviside taper
tension control through a heaviside factor (Φ), in the winding
process, which is the final section of the roll-to-roll or web handling
system.

Technical Solution

[0034]To achieve the above objects, in one aspect, the present invention
provides a method for controlling taper tension in the winding section of
a web handling system, the method comprising the steps of: (a) inputting
into PLC a material to be used in initial operation, along with operating
tension and velocity; (b) transmitting the diameter value (data) of a
roll, currently being wound, from a motor driver into the PLC; (c)
establishing in the PLC a taper value (reduction in operating tension) to
be achieved; (d) determining in the PLC the type of taper tension profile
in consideration of the radial stress distribution and telescoping within
the roll on the basis of data, including initial operating tension, roll
diameter and taper value, which are collected from steps (a) to (c); and
(e) producing in the PLC an electrical signal for taper tension according
to the taper type determined in step (d) to control the pressure of the
air cylinder of a dancer system through an E/P converter and to control
taper tension through a tension meter or a loadcell, in which the taper
tension control method satisfies the following equation:

[0035]wherein the hybrid factor serves to select one of a linear taper
tension profile and a hyperbolic taper tension profile based on an value
between 1 and 0 and produces a taper tension profile, which is an
intermediate type between the linear taper tension profile and the
hyperbolic taper tension profile.

[0036]In another aspect, the present invention provides a method for
controlling taper tension in the winding section of a web handling
system, the method comprising the steps of: (a) inputting into PLC a
material to be used in initial operation, along with operating tension
and velocity; (b) transmitting the diameter value (data) of a roll,
currently being wound, from a motor driver into the PLC; (c) establishing
in the PLC a taper value (reduction in operating tension) to be achieved;
(d) determining in the PLC the type of taper tension profile in
consideration of the radial stress distribution and telescoping within
the roll on the basis of data, including initial operating tension, roll
diameter and taper value, which are collected from steps (a) to (c); and
(e) producing in the PLC an electrical signal for taper tension according
to the taper type determined in step (d) to control the pressure of the
air cylinder of a dancer system through an E/P converter and to control
taper tension through a tension meter or a loadcell, in which the taper
tension control method satisfies the following equation:

[0037]wherein the taper tension profile is changed depending on the value
of Φ.

[0038]In the method of the present invention, the type of linear taper
tension profile is changed to the type of hyperbolic taper tension
profile depending on the value of Φ.

[0039]In still another aspect, the present invention provides a method for
controlling taper tension in the winding section of a web handling
system, the method comprising the steps of: (a) inputting into PLC a
material to be used in initial operation, along with operating tension
and velocity; (b) transmitting the diameter value (data) of a roll,
currently being wound, from a motor driver into the PLC; (c) establishing
in the PLC a taper value (reduction in operating tension) to be achieved;
(d) determining in the PLC the type of taper tension profile in
consideration of the radial stress distribution and telescoping within
the roll on the basis of data, including initial operating tension, roll
diameter and taper value, which are collected from steps (a) to (c); and
(e) producing in the PLC an electrical signal for taper tension according
to the taper type determined in step (d) to control the pressure of the
air cylinder of a dancer system through an E/P converter and to control
taper tension through a tension meter or a loadcell, in which the taper
tension control method satisfies the following equation:

[0040]In the method of the present invention, the hybrid factor serves to
select one of a linear taper tension profile and a hyperbolic taper
tension profile at an value between 1 and 0 and produces a taper tension
profile, which is an intermediate type between the linear taper tension
profile and the hyperbolic taper tension profile.

[0041]Also, the taper tension profile is changed depending on the value of
Φ.

ADVANTAGEOUS EFFECTS

[0042]According to the present invention, a more uniform, high-quality
wound roll can be produced by stabilizing radial stress distribution and
minimizing telescoping, which is the lateral displacement of material in
a winding section, using hybrid taper tension control through a hybrid
factor (α (alpha)).

[0043]In addition, a heaviside taper tension control method designed on
the basis of a hybrid taper tension profile allows a more stable,
high-quality wound roll to be produced in consideration of not only
radial stress distribution, but also the minimization of telescoping,
which is the lateral displacement of material in the winding section.

DESCRIPTION OF DRAWINGS

[0044]FIG. 1 is a schematic diagram of the tension T acting on the web and
roll.

[0051]FIG. 8 is a photograph showing a telescoping phenomenon in a prior
wound roll.

[0052]FIG. 9 is a photograph showing a starring phenomenon in a prior
wound roll.

[0053]FIG. 10 shows the operation and construction of a system for
controlling taper tension in the winding section of a web handling system
according to a preferred embodiment of the present invention.

[0054]FIG. 11 is an operational flowchart for controlling taper tension in
the winding section of a web handling system according to a preferred
embodiment of the present invention.

[0055]FIG. 12 shows the construction of a dancer system which is used to
control taper tension.

[0056]FIG. 13 shows a tension meter which is used to control taper
tension.

[0057]FIG. 14 shows a profile for hybrid taper tension profile according
to a first preferred embodiment of the present invention.

[0088]Hereinafter, preferred embodiments of the present invention will be
described in detail with reference to the accompanying drawings.

[0089]FIG. 10 shows the operation and construction of a system for
controlling taper tension in the winding section of a web handling system
according to a preferred embodiment of the present invention, FIG. 11 is
an operational flowchart for controlling taper tension in the winding
section of a web handling system according to a preferred embodiment of
the present invention, FIG. 12 shows the construction of a dancer system
which is used to control taper tension, and FIG. 13 shows a tension meter
which is used to control taper tension.

[0090]With respect to the operation of the external system of a web
handling (or roll-to-roll) system, as shown in FIG. 10, a material to be
used in an initial operating stage, and operating tension and velocity,
are set in PLC, which is a main controller. Herein, the PLC receives the
diameter value of a winding roll from a motor driver. An electrical
signal for taper tension from the set value is inputted into an E/P
converter to control taper tension through the change in the pressure of
the air cylinder of a dancer system and through a tension meter or a
loadcell (b). Due to the change in the pressure of the air cylinder, the
tension of the material is reduced through a dancer roll connected to the
air cylinder, and desired taper tension is achieved (c).

[0091]The operation of an internal logic for the operation of the external
system will now be described with reference to FIGS. 10 and 11.

[0092]First, a material to be used in an initial operating stage, and
operating tension and velocity are decided (step 1).

[0093]Then, the current diameter value (data) of the winding roll is
transmitted from a motor driver, an external controller, into PLC, a main
controller (step 2).

[0094]Then, a taper value to be achieved (reduction in operating tension)
is set (step 3).

[0095]Then, based on the data (initial operating tension, roll diameter,
taper value, etc.) collected up to the current time, a taper type
(heaviside taper tension) is determined in consideration of the radial
stress distribution and telescoping within the roll (step 4).

[0096]Finally, the main controller PLC receives the signal of step (4) to
produce an electrical signal for taper tension, and the E/P converter
receives the electrical signal from the PLC to reduce the internal
pressure of the air cylinder of the dancer system (step 5). Herein, the
tension of the material is reduced through the dancer roll connected to
the air cylinder, and desired taper tension is achieved through the
tension meter or loadcell.

[0097]The tension meter shown in FIG. 13 is a mechanical device, which is
placed on the axial portion of the roll to indicate the tension of the
material passing on the roll, and it is also called "loadcell". A strain
gauge is disposed in the loadcell, such that a load being applied to the
roll can be found from the change in the strain gauge. Desired taper
tension can be achieved through not only the dancer system, but also the
tension meter.

[0098]The results of computer simulation of hybrid tension control by such
external operation and internal logic are shown in FIG. 14, and the
results of computer simulation of heaviside taper tension control by such
external operation and internal logic are shown in FIG. 18. The hybrid
tension control method can indicate various taper tension profiles
through the change in the hybrid factor (α). Specifically, if the
hybrid factor is zero (0), it can mean the hyperbolic taper tension
profile, and if the hybrid factor is 1, it can mean the linear taper
tension profile.

[0099]In addition, as shown in FIG. 18, the heaviside taper tension
control method is a taper tension control method in which the linear
taper tension profile changes to the hyperbolic taper tension profile
based on the hybrid taper tension control method using a heaviside
function (Φ) in the beginning of rewinding, where great lateral
displacement occurs. Experimental verification for the hybrid taper
tension profile and the heaviside taper tension profile were conducted,
and the experimental results are shown in FIGS. 20 to 22.

[0100]As described above, in order to solve the prior problems associated
with telescoping (FIG. 8) and starring (FIG. 9), the present inventors
propose a hybrid taper tension control method, which can be derived from
the prior taper tension control method and hyperbolic taper tension
control method through the change in hybrid factor (α) (Math Figure
13). In addition, the present inventors propose a heaviside taper tension
control method (Math Figure 16) on the basis of the hybrid taper tension
control method in order to stabilize stress distribution in a wound roll
and to minimize telescoping in the wound roll. Herein, the heaviside
taper tension control method can control tension at a desired radial
position.

[0101]Hereinafter, a hybrid taper tension control method and heaviside
taper tension control method according to a preferred embodiment of the
present invention will be described in further detail.

[0102]The results of FIG. 4 show that the derivative (rate of the
variation) of effective residual stress (ERS) according to the wound roll
radius can be obtained lower by the hyperbolic taper tension profile than
the linear taper tension profile. As shown in FIGS. 15 and 16, a small
derivative of ERS makes the radial stress distribution lower. These
results indicate that the hyperbolic taper tension profile is more
advantageous in view of radial stress distribution. However, as shown in
FIG. 7, the possibility and magnitude of telescoping of a wound roll near
the outside of the core are much higher than when the taper tension
profile is applied during the winding process.

[0103]As shown in FIGS. 16 and 17, the linear taper tension profile is
advantageous for preventing the telescoping of the wound roll in the
beginning of the winding process, and the hyperbolic taper tension
profile is advantageous in terms of the radial stress distribution.

[0104]The hybrid taper tension profile can be designed to take advantages
of each of the linear and hyperbolic taper tension profiles by combining
both algorithms. Math Figure 12 shows the mathematical model of the
hybrid taper tension model. Also, the models of ERS and radial stress
distribution of a wound roll for the hybrid taper tension profile are
shown in Math Figures 13 and 14:

[0105]The hybrid factor (α) in Math Figure 13 determines the
contribution to both of the liner and hyperbolic taper tension profiles
in designing a new hybrid taper tension profile. α values of 1 and
0 indicate linear and hyperbolic taper tension profiles, respectively, as
shown in FIG. 8.

[0106]FIGS. 15 to 17 show simulation results of the ERS, radial stress
distribution, and induced telescoping of a wound roll when the hybrid
taper tension profile is applied to a winding process. From these
simulation results, it can be found that the use of the hybrid taper
tension profile resulting from the control of the hybrid factor can
reduce the magnitude of radial stress distribution and telescope in a
wound roll within the satisfying boundary.

[0107]FIG. 17 shows that lateral displacement is very different according
to the types of taper tension profile. In the beginning of rewinding
(r<2), the telescoping problem is very serious. After that (r>2),
the radial stress distribution is so important (FIGS. 16 and 17). In
order to minimize telescoping and to optimize radial stress distribution,
a heaviside taper tension profile is proposed as shown in Math Figure 16:

[0108]wherein means a heaviside function. In Math Figure 16, the type of
taper tension profile is changed according to increasing build-up ratio
(r). Namely, the type of taper tension profile can be changed by the
heaviside function (Φ) according to increasing build-up ratio (r) as
shown in FIG. 18.

[0109]FIG. 19 shows a roll-to-roll system, used for the experiment in the
present invention and composed of unwinding, in-feeding, printing,
out-feeding and winding sections. The main experimental conditions are
shown in Table 1 below.

[0110]FIG. 15 shows four types of taper tension profiles. From the
experimental results, it can be seen that the taper tension in the
winding system follows the reference tension profile. The type of taper
tension profile is determined by the hybrid factor (α), as shown in
Math Figure 12 and the heaviside function (Φ) as shown in Math Figure
16.

[0111]FIG. 16 shows experimental results of the radial stress
distribution. In FIGS. 16 and 17, the correlation between taper tension
and radial stress distribution is confirmed. Finally, the radial stress
distribution for the linear taper tension profile is larger than for
other taper tension profiles. These results indicate that the hyperbolic
taper tension profile is more effective for preventing starring and
minimizing telescoping. However, the hyperbolic taper tension profile may
cause telescoping as shown in FIG. 17(b). The telescoping in FIG. 17 was
measured by EPS (edge position sensor).

[0112]Namely, it is necessary to find out an optimal taper tension profile
for preventing starring and minimizing telescoping. For this purpose, a
heaviside tension profile is proposed in the present invention. The
experimental results show that the proposed heaviside taper tension
profile is very effective for minimizing the telescoping problem and for
preventing the starring problem as shown in FIGS. 15 and 16.

[0113]In the present invention, the effects of taper tension profiles
during roll winding were analyzed through the radial stress distribution
and the telescoping of a roll. In addition, the hybrid taper tension
profile and the heaviside taper tension profile were newly proposed, and
the performance of the proposed heaviside taper tension profile was
verified through computer simulations and experiments.

[0114]The present inventors have developed the mathematical model, which
allows the types of linear taper tension profile and hyperbolic taper
tension profile, which are the prior methods for controlling taper
tension in the winding section, to be changed through the hybrid factor
(α). On the basis of this mathematical model, the present inventors
have developed the heaviside taper tension control method for optimizing
radial stress distribution and minimizing telescoping.

[0115]According to the present invention, the heaviside taper tension
control method designed on the basis of the hybrid taper tension profile
can produce a more uniform, high-quality wound roll not only by
stabilizing radial stress distribution, but also minimizing telescoping,
which is the lateral displacement of material in the winding section.

INDUSTRIAL APPLICABILITY

[0116]The present invention considers the influence of telescoping, which
has not been considered in the taper tension control method, which is
actually carried out in the industrial fields. The method of changing the
types of linear taper tension profile and hyperbolic taper tension
profile, which are used in the prior art, should be considered to be
included in the scope of the present invention. Particularly, the method
of changing the type of taper tension control to reduce telescoping in
the beginning of rewinding should also be considered to be included in
the scope of the present invention, because the heaviside taper tension
control used to reduce telescoping is performed through the change of the
type of taper tension control.